Chapter 11.6, Problem 20PPS

To determine

To find: the area of the entire sail.

Answer to Problem 20PPS

The area of entire sail is 490 square ft.

Explanation of Solution

Given information:

The sail at the right is formed from two congruent triangles.

Calculation:

Consider the figure

  

The two triangles form by sail is $\Delta ABD$ and $\Delta ACD$ .

If two triangles are congruent then their corresponding angles and their corresponding sides are congruent.

Since $\Delta ABD\cong \Delta ACD$ , so their corresponding sides are congruent.

From figure, the corresponding sides are

  $\begin{array}{c}AB\cong AC\\ BD\cong CD=17.5\\ DA\cong DA=28\end{array}$

Thus,

  $\begin{array}{c}BC=BD+CD\\ =17.5+17.5\\ =35\end{array}$

The area $A$ of a triangle is given by the formula

  $A=\frac{1}{2}\times b\times h$

Where $b$ is the base of the triangle and $h$ is the height of the triangle.

From figure,

  $b=BC=35$ and $h=AD=28$

The area $A$ of the triangle $\Delta ABC$ is

  $\begin{array}{c}A=\frac{1}{2}\times b\times h\\ =\frac{1}{\cancel{2}}\times 35\times \cancel{28}\\ =35\times 14\\ =490\end{array}$

Therefore, the area of entire sail is 490 square ft.